Factor model is an appealing and effective analytic tool for high-dimensional time series, with a wide range of applications in economics, finance and statistics. This paper develops two criteria for the determination of the number of factors for tensor factor models where the signal part of an observed tensor time series assumes a Tucker decomposition with the core tensor as the factor tensor. The task is to determine the dimensions of the core tensor. One of the proposed criteria is similar to information based criteria of model selection, and the other is an extension of the approaches based on the ratios of consecutive eigenvalues often used in factor analysis for panel time series. Theoretically results, including sufficient conditions and convergence rates, are established. The results include the vector factor models as special cases, with an additional convergence rates. Simulation studies provide promising finite sample performance for the two criteria.

翻译：系数模型是高维时间序列的一个具有吸引力和有效的分析工具,在经济学、金融和统计方面应用范围很广,本文件为确定高因数模型的因数数量制定了两个标准,即所观测的强时序列的信号部分假定塔克分解为核心数分解为因素数分解。任务是确定核心数分解的维度。提议的标准之一与基于信息的模式选择标准相似,另一个是扩大基于小组时间序列要素分析中经常使用的连续无源值比率的方法。理论上的结果,包括充分的条件和趋同率,已经确定。结果包括作为特殊情况的矢量要素模型,加上额外的趋同率。模拟研究为两种标准提供了有希望的有限抽样性能。